Question

Problema 32 dacă se poate până vineri, vă rog

Answer 1

a)
x=√3+√3²+√3³+√3⁴+...+√3²⁰¹⁹
x√3=√3²+√3³+√3⁴+...+√3²⁰¹⁹+√3²⁰²⁰
x√3-x=√3²+√3³+√3⁴+...+√3²⁰¹⁹+√3²⁰²⁰-(√3+√3²+√3³+√3⁴+...+√3²⁰¹⁹)
x√3-x=√3²⁰²⁰-√3
x√3-x=3¹⁰¹⁰-√3            
x+3¹⁰¹⁰=x√3+√3
x+3¹⁰¹⁰=√3(x+1)

b)
2x/(√3+1) +√3 =
x√3-x=3¹⁰¹⁰-√3            x(√3-1)=3¹⁰¹⁰-√3       x=(3¹⁰¹⁰-√3)/(√3-1) 
[2 × (3¹⁰¹⁰-√3)/(√3-1)] /(√3+1) +√3 =
=[2 × (3¹⁰¹⁰-√3)]/(√3-1)(√3+1) +√3 =
=[2 × (3¹⁰¹⁰-√3)]/(3-1) +√3 =
=2 × (3¹⁰¹⁰-√3)/2 +√3 =
=3¹⁰¹⁰-√3 +√3 =
=3¹⁰¹⁰=
=(3⁵⁰⁵)²